 In addition to the 31 ​cent-per-piece trade​ discount, the customer also receives a one half %

 cash discount. Calculate the rebate and cash discount on a​ 30,000-piece-per-month order, and then find the net price. The cash discount of one half %

 is taken after the rebate is applied.

We need to calculate both the rebate and the cash discount for a 30,000-piece order, then find the net price.

### Step 1: Calculate the rebate (trade discount)
The trade discount is 31 cents per piece, and the customer is ordering 30,000 pieces.

\[
\text{Rebate} = 0.31 \, \text{(dollars per piece)} \times 30,000 \, \text{pieces}
\]

\[
\text{Rebate} = 9,300 \, \text{dollars}
\]

### Step 2: Apply the rebate to the original price
We now need to subtract the rebate from the total price of the order before applying the cash discount. The original price (before rebate) would be:

\[
\text{Original Price} = 30,000 \, \text{pieces} \times \text{Price per piece}
\]

However, since the price per piece is not provided, we will refer to the total rebate as $9,300 for the purpose of applying the cash discount.

### Step 3: Calculate the cash discount
The cash discount is 0.5%, but it's applied **after** the rebate is deducted. If we let $ P $ represent the original total price of the 30,000 pieces, then the price after the rebate is $ P - 9,300 $.

The cash discount is:

\[
\text{Cash Discount} = 0.005 \times (P - 9,300)
\]

### Step 4: Calculate the net price
Finally, the net price is the price after both the rebate and the cash discount are applied:

\[
\text{Net Price} = (P - 9,300) - \text{Cash Discount}
\]

\[
\text{Net Price} = (P - 9,300) - 0.005 \times (P - 9,300)
\]

This formula gives the final net price after both discounts. To get a specific numeric value for the net price, the price per piece would be required.

Would you like more details or clarifications?

Here are 5 related questions to expand this:
1. How would the result change if the trade discount were different?
2. What is the effect of a higher order quantity on the cash discount?
3. How does the order size impact the overall rebate?
4. What if the cash discount were 1% instead of 0.5%?
5. How would pricing be affected if there was an additional type of discount?

**Tip:** Always apply trade discounts before cash discounts to get the most accurate final price.

In addition to the 31 ​cent-per-piece trade​ discount, the customer also receives a one half % cash discount. Calculate the rebate and cash discount on a​ 30,000-piece-per-month order, and then find the net price. The cash discount of one half % is taken after the rebate is applied.

Learn how to calculate the rebate and cash discount on a 30,000-piece order with a 31 cent-per-piece trade discount and a 0.5% cash discount. This problem involves key mathematical concepts like discount calculations, percentages, and applying rebates to find the net price. Suitable for students in Grades 10-12.

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